[maxime borges] has such a perfect setup that involves a HDMI 4: ... HDMI switch, and if you’re looking for references, we’ve covered a good few hacks doing that as part of building a KVM.

Today, KVM switchers are a bit more complicated than a simple rotary switch. We’re not dealing with VGA anymore — we have HDMI muxes ... with a 74HC4052 dual 4:1 analog mux.